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From collective rhythm to adaptive synchronization of neural activity

By Debin Huang

Abstract

A novel viewpoint, i.e., adaptive synchronization, is proposed to explore collective rhythm observed in many complex, selforganizing systems. We show that a simple adaptive coupling is able to tip arrays of oscillators towards collective synchronization. Two arrays of simple electrically coupled Hindmarsh-Rose chaotic neurons are used to illustrate cooperative dynamics of neural activity like the central pattern generators, which supplies a new idea for biological experiments and numerical simulations. The results indicate that such small-world adaptive coupling may be a universal essence of the collective rhythm observed in the natural world. PACS number(s): 87.10.+e; 05.45.-a; 84.35.+i Today one of the main unsolved problems in science is how to apperceive and study complex, self-organizing systems. A puzzling characteristic in these systems is the spontaneous collective rhythm, i.e., so-called collective synchronization. This remarkable phenomenon has been observed extensively in the natural world, ranging from inorganic systems to organic systems, e.g., Christiaan Huygens ’ two synchronization clocks, wobbly bridges, the oscillating uniformly Josephson junctions, the Bose-Einstein condensate (BEC), emerging coherence in chemical oscillators, fireflies synchronizing spontaneously their flashes, self-synchronization of the cardiac pacemaker cells, the cooperative pattern in network of neurons, animals ’ gaits, groups of women with the mutually synchronized menstrual cycles, an audience clapping in sync, and coherent moving states recently observed in highway traffic, etc [1]. In the collective rhythm, each individual itself executes two different behaviors, i.e., periodic oscillating and aperiodic (i.e., chaotic) oscillating. The collective rhythm of periodic oscillators emerges in many fields, while the collective chaotic synchronization is observed in the network of neurons and two weakly coupled BECs, etc

Year: 2004
OAI identifier: oai:CiteSeerX.psu:10.1.1.235.1413
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